BAGHDAD—Iraq's outgoing prime minister, Nouri al-Maliki, appears to have dropped his quixotic struggle to remain in power over the past week and is resigned instead to remaining a member of parliament insulated from prosecution.

Fears that Mr. Maliki might play the spoiler in the new government have largely receded since his initial reaction to the appointment of Haider al-Abadi to replace him. The night before Mr. Abadi's...